Market targeting and information sharing with social influences in a luxury supply chain

Transportation Research Part E 133 (2020) 101822

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Market targeting and information sharing with social influences in a luxury supply chain

T

Qiao Zhanga, , Jing Chenb, Georges Zaccourc ⁎

a b c

School of Management, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, China Rowe School of Business Dalhousie University, Halifax NS B3H 4R2, Canada GERAD, HEC Montréal, Montreal H3T 2A7, Canada

ARTICLE INFO

ABSTRACT

Keywords: Social influences Market-targeting strategy Luxury supply chain Information sharing

We consider a luxury supply chain in which one Stackelberg manufacturer sells products to consumers through a retailer. Driven by exclusivity or conformity, consumers are classified as either snobs or conformists, with uncertain preferences about the product. The manufacturer can obtain a private signal on this preference, while the retailer cannot. Results show that the manufacturer makes different market-targeting schedules in response to different signals. Interestingly, the manufacturer may benefit from either a no-information, a private-information, or an information-sharing policy, depending on its market-targeting strategy. Not sharing the manufacturer’s information, however, is preferred by the retailer.

1. Introduction Consumers are inclined to pay more attention to psychological benefits than functional benefits when purchasing a product, especially when it is a luxury or conspicuous product (Castaño et al., 2008; Joshi et al., 2009; Huang et al., 2018). Some consumers (such as snobs), driven by the psychology of exclusivity, perceive a product as having a lower valuation if it is widely consumed in the market. Meanwhile, other consumers (such as conformists) prefer to buy a product when it is highly consumed, driven by the psychology of conformity. As pointed out by Shen et al. (2017) and Zheng et al. (2012), snobs and conformists are known to coexist in luxury consumption. The corresponding exclusivity and conformity effects (known as social influences) represent universal human desires (Tsai et al., 2013), as first proposed by Leibenstein (1950). The snob and conformist effects in luxury consumption were identified and tested in an empirical study by Kastanakis and Balabanis (2014). Social influence resulting from the distinct behaviors of two consumer groups in luxury market always makes consumer portfolio management particularly difficult. Specifically, to give snobs good service, a luxury firm may need to limit its quantity of product or to price its product high. For instance, Hermès had a two-year waiting list for its Birkin handbag, priced at more than $6,000 (Amaldoss and Jain, 2008). The high price may well satisfy some snobs’ pursue for exclusivity, however, it may loss more market share from conformists since they are more sensitive to price than snobs (Zheng et al., 2012). Consequently, luxury firms face a conundrum in their marketing decisions, in terms of balancing pricing and the management of their target clientele. In addition, the heterogeneity and uncertainty of consumer preference regarding a given product add another dimension that impacts consumer purchasing behavior. Given these consumer behaviors, it is interesting to investigate the pricing and market-targeting strategies of firms in a luxury supply chain. To face the uncertainty of consumer preference regarding a product, manufacturers increasingly tend to conduct R&D to obtain

⁎

Corresponding author. E-mail addresses: [email protected] (Q. Zhang), [email protected] (J. Chen), [email protected] (G. Zaccour).

https://doi.org/10.1016/j.tre.2019.101822 Received 14 September 2019; Received in revised form 9 December 2019; Accepted 9 December 2019 1366-5545/ © 2019 Elsevier Ltd. All rights reserved.

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better market demand forecasts to fine tune their production planning. As the downstream or franchised stores of manufacturers, retailers are less able to acquire information about demand, and have to rely on the upstream manufacturers for that information (Mohr and Sohi, 1995). This phenomenon is especially common in a luxury supply chain when a luxury manufacturer distributes its product through the selected large luxury department stores or major e-retailers. In such a case, the department stores or e-retailers sell multiple luxury brands and pay little attention to consumer preference for a specific luxury brand. Only the luxury manufacturers (brand owners), such as Burberry, Prada, and Coach, are willing to make huge R&D investments to gauge consumer preference. For example, Burberry is always trying to find new ways to engage customers to improve its personalization capabilities. In June 2019, it invited UK university students to advise it on the “trench coat of the future”. Some of the ideas proposed by students will be adapted and customized for different stages of a customer’s life (e.g., size, fitness, and trend changes) to keep the product in use longer.1 Based on this asymmetric information between the luxury product manufacturer and the retailer, and given different consumer preferences, we are interested in whether or not the manufacturer has an incentive to share its information with its retailer. Against this backdrop, we will address the following research questions in this paper. (1) How should the channel members make pricing strategies for consumer portfolio management? (2) How do the social influences impact the manufacturer’s market-targeting and the pricing strategies and profits of both the manufacturer and the retailer in the supply chain? (3) What is the manufacturer’s optimal information policy, and is it also preferred by the retailer? To address these research questions, we develop a signaling game for a manufacturer and retailer in a luxury supply chain, facing two groups of consumers in the market: snobs and conformists. Each consumer group impacts the other’s purchasing behavior. Consumers are uncertain regarding their product preference. We investigate the manufacturer’s pricing strategy with its associated market-targeting strategy in the presence of the interaction of the two consumer groups. The manufacturer has the capability to forecast information on consumers’ willingness-to-pay (WTP) and can choose whether or not to share its information with the retailer. Without information sharing, the manufacturer has to bear the signaling cost resulting in a decrease in the profit due to the distorted downward wholesale price in the signaling game. This cost can be mitigated by information sharing. Sharing information, however, may impact the manufacturer’s equilibrium strategy and profit, suggesting that the manufacturer should carefully evaluate the tradeoff when it makes decisions. Upon this, we derive the equilibrium pricing strategies in the presence of market segmentation and we study the impacts of social influences on equilibria. The preferences of both the manufacturer and the retailer on the information policy (no-information, private-information, and information-sharing) are analyzed. We find that, when both markets are captured, if the fraction of snobs is larger than one half, the social influence softens the vertical price competition between the manufacturer and the retailer, as both the manufacturer and the retailer will increase the equilibrium prices. However, if the fraction of snobs is less than one half, the social influences have a negative effect on equilibrium prices, unless the price sensitivity is less than a certain threshold. The manufacturer may make different market-targeting schedules when it receives different signals, but it will not switch from targeting the conformist market when it observes a high signal to targeting the snob market when it observes a low signal. Interestingly, we find that the manufacturer does not always benefit from sharing its information with the retailer, although this information sharing helps avoid the signaling cost. The manufacturer can benefit from either a no-information, a private-information, or an information-sharing policy, depending on its market-targeting strategy. Not sharing the manufacturer’s information, however, is a dominant policy for the retailer. The contributions of this paper are as follows. First, while considering asymmetric information in a supply chain, we develop a signaling game model to discuss the impacts of social influences and information policy on channel members’ pricing strategies and market-targeting strategies. This complements the research on signaling games in the presence of social influences. Second, we discuss the preferences of the manufacturer and the retailer regarding the information policy with social influences, which offers some interesting insights on information management for the supply chain management literature. The remainder of this work is organized as follows: Section 2 reviews the related literature and Section 3 describes the model. Section 4 presents the equilibrium pricing strategies under different market-targeting strategies and examines the impacts of system parameters on the equilibria. The preferences of the manufacturer and the retailer regarding the information policy are discussed in Section 6. Section 7 briefly concludes and proposes some extensions for future work. 2. Literature review Our study relates to two research streams, namely, social influences in luxury supply chain management, and signaling games. Social influence refers to how an individual’s decisions are impacted by others when they exchange and share information with social network members and update their expectations regarding the outcome of their own choices (Kim et al., 2017). There are two specific types of social influence: the exclusivity effect and the conformity effect, which correspond to one of the two social groups, i.e., snobs (dissociative group) and conformists (membership group), respectively (Escalas and Bettman, 2005). Snob consumers are less inclined to choose a product as the number of its purchasers increases (Gao et al., 2016; Thomas and Vinuales, 2017), while conformists have the opposite preference. Conformity is commonly known as the herding effect, describing decisions that are based on collective actions in a market rather than on personal beliefs and information (Papapostolou et al., 2017). The evidence of social 1

https://www.burberryplc.com/en/news/news/responsibility/2019/b-innovative–burberry-invites-university-students-to-design-the0.html 2

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influences on luxury (or conspicuous product) consumption has been largely established (Li et al., 2012; Mason, 1984). Han et al. (2010) demonstrate that the preference of a particular market segment for luxury products is closely related to the preferences of other segments. Leibenstein (1950) first summarized three luxury consumption effects–bandwagon (conformist), snob, and Veblenian for conspicuous consumption. According to Chinese consumers’ characteristics, Lu and Pras (2011) propose groups of Chinese luxury consumers, which also include snobs and conformists. The studies on luxury with social influences have been from both the empirical and mathematical modeling perspectives. In empirical studies, Kastanakis and Balabanis (2014) examine the impact of various individual differences on consumers’ propensity to engage in two forms of luxury consumption behavior: bandwagon (conformist) and snob effects. They show that luxury consumption should not be treated unidimensionally but rather disaggregated into snob and bandwagon consumption patterns. Tsai et al. (2013) examine the effects of Chinese consumers’ American and Chinese cultural identifications on their snob and bandwagon luxury-brand preferences. They find that in Chinese consumers, an affinity with individualistic American culture is positively associated with a snob luxury preference, while an identification with collectivistic Chinese culture is positively associated with bandwagon luxury consumption. Ste¸pień (2018) applies a mixed method with an esurvey and interviews to explore the grounds of bandwagon and snob interconnectedness. The results show that consumers can exhibit both bandwagon and snob inclinations in luxury consumption. In studies with mathematical modeling, Amaldoss and Jain (2005a) study the pricing issue for conspicuous products in a monopoly with social influences, and examine how purchasing decisions are affected by the desire for exclusivity and conformity. Amaldoss and Jain (2005b) further extend the study on this issue to a competitive environment by examining pricing strategies for a duopoly. They show that the desire for uniqueness leads to higher prices and firm’s profit, but a desire for conformity leads to an opposite result. Agrawal et al. (2015) focus on durability in product design for conspicuous products, considering consumers’ exclusivity, and find that firms benefit from designing products with greater durability in conjunction with a high-price and low-volume introduction strategy. Chiu et al. (2018) investigate optimal consumer portfolio and optimal advertising-budget allocation for a luxury good, while considering social influences, and find that the optimal strategy is to allocate all the advertising budget to one group of consumers only (snob group or conformist group). Other studies related to social influences in a luxury supply chain include, e.g., Shen et al. (2017), Tereyagˇogˇlu and Veeraraghavan (2012), and Zheng et al. (2012). Our research also relates to signaling games in operations management and marketing. Private information on cost, product quality, or demand is common in a supply chain, and may signal through pricing. Jiang et al. (2014) discuss pricing strategies and the market outcome in a service market where the provider has two sources of private information about its type (whether ethical or selfinterested) and about the consumer’s condition (whether serious or minor). Supposing that the reseller has private information on demand, Li et al. (2013) explore the impact of supplier encroachment on equilibrium solutions, and conclude that double marginalization is amplified by the supplier’s encroachment. Jiang et al. (2016) concentrate on information sharing in a distribution channel where the manufacturer possesses better demand information than the retailer. The equilibrium outcomes under three informationsharing schemes (no information sharing, voluntary information sharing, and mandatory information sharing) are characterized and compared. It is shown that the retailer prefers the no-sharing format whereas the manufacturer is better off with a mandatory-sharing format. Zhen et al. (2019) consider herding and word-of-mouth (WOM) effects during the launch of a new product, and investigate the impacts of consumer behavior on the existence of separating (signaling quality) and pooling (hiding quality information) equilibria in a two-period advertising signaling model. They find that, if the strength of WOM or the unit advertising cost increases, or if the herding effect decreases, a pooling equilibrium dominates; otherwise, a separating equilibrium dominates. Sun et al. (2019) develop a signaling game to examine a manufacturer’s encroachment problem with the cost reduction decision under either asymmetric or symmetric demand information. They find that encroachment motivates the manufacturer to invest more in cost reduction if, and only if, the direct selling channel is relatively efficient. Other signaling issues related to product quality are dealt with in, e.g., Moorthy and Srinivasan (1995), Yu et al. (2014), and Chen and Jiang (2016). In addition, some studies focus on cost signaling, such as Guo (2015), Guo and Jiang (2016), and Zhang et al. (2019). Studies in signaling game (e.g., Jiang et al. (2016)) show that without information sharing, the manufacturer incurs a signaling cost due to the distorted downward wholesale price. Differing from the above studies, we find that interestingly, the manufacturer may benefit from either a no-information, a private-information, or an information-sharing policy, depending on its market-targeting strategy. The closest studies to ours are Shen et al. (2017), Chiu et al. (2018), and Jiang et al. (2016). Shen et al. (2017) consider a luxury supply chain consisting of one supplier and one online retailer who provides differentiated services to two consumer groups (snobs and conformists). They examine the effects of demand changes on the equilibrium price and service strategies, and further discuss the channel coordination issue. Our paper also takes a similar supply chain structure and considers two social influences, but we focus on the manufacturer’s market-targeting strategy and information-sharing scheme with asymmetric demand information. Considering a luxury fashion firm serving two consumer groups (snobs and conformists), Chiu et al. (2018) investigate the optimal customer portfolios and the optimal budget allocation problem, and show that the optimal strategy is to allocate all of the advertising budget to one consumer group only. This is an optimality issue and only focuses on advertising allocation, but not pricing. Unlike their work, ours develops a game-theoretical model for a luxury supply chain and focuses on pricing and market-targeting strategies. In the area of information sharing in distribution channels, Jiang et al. (2016) suppose that the manufacturer possesses better demand-forecasting information than the retailer. They consider three information-sharing formats: no information sharing, voluntary information sharing, and mandatory information sharing, and investigate the firms’ preferences regarding these formats. It is shown that the retailer prefers the no-sharing format whereas the manufacturer prefers the mandatory-sharing format. Adopting a similar information structure to the one in Jiang et al. (2016), our paper takes consumers’ social influences into account, which significantly impacts the manufacturer’s information-sharing decision. We show that the manufacturer may prefer a no-information, a private-information, or an informationsharing policy depending on its market-targeting strategy: this result differs from the findings of Jiang et al. (2016). 3

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3. Model We consider a luxury supply chain, where a manufacturer distributes its luxury product through a selected retailer (such as a large luxury department store or e-retailer). The manufacturer and the retailer need to decide the wholesale price w and the retail price p, respectively. There are two groups of consumers in the market: snobs, at a fraction of , and conformists, at a fraction of 1 . Snobs pursue exclusivity, as they perceive a product as less valuable if it is purchased by many people in the market. Conformists, however, prefer to imitate other consumers’ actions when making their purchasing decisions. The co-existence of snobs and conformists in the luxury market has not only been proved empirically (Kastanakis and Balabanis, 2014; Leibenstein, 1950; Lu and Pras, 2011), but has also been considered theoretically in the literature (Amaldoss and Jain, 2005a; Chiu et al., 2018; Shen et al., 2017). Note that neither group knows the exact sales volume of the product, but will estimate sales based on its observations and experience. The consumers’ willingness to pay (WTP) for the product is , which is assumed to be either high ( = h ) or low ( = l < h ), reflecting the consumers’ heterogeneous perceived valuation of the product. The assumption of two demand states is very common in the operations literature (e.g., Huang et al. (2018), Jiang et al. (2016), Song et al. (2017)). As in Amaldoss and Jain (2015), we suppose that a consumers’ group category and its perceived valuation of the product are independent, i.e., the perceived valuations of the product by snobs and conformists are the same. As in Amaldoss and Jain, 2015, we assume that these two perceived product valuations have equal ex ante probabilities, i.e., Pr( h ) = Pr( l ) = 1/2 . Based on the assumption in Amaldoss and Jain (2005a) that all rational consumers would have the same expectation about the number of consumers who will buy the product, Chiu et al. (2018) proved that the demands for these two groups are interdependent with two social effects: the conformity effect and the exclusivity effect. That is, a higher expected demand from snobs will lead to a higher demand from conformists (conformity effect), while a higher expected demand from conformists generates a lower demand from snobs (exclusivity effect). To capture these mutual social influences between the two groups, the demands from snobs (Ds ) and conformists (Dc ) are specified as follows:

bE [Dc ],

(1)

p + q + E [Ds],

(2)

Ds = A

p+ q

Dc = (1

)A

where A is the market potential, , b, and are positive parameters, and 0 < < 1, reflecting that snobs are less sensitive to price than are conformists (see, e.g., Zheng et al. (2012)). q is a demand sensitivity parameter, reflecting the degree of sensitivity of the demand to the customers’ valuation , where q [0, 1]. If q = 0, then the market’s demand is insensitive to the customers’ valuation of the product. The higher the value of q, the more the market’s demand is sensitive to the customers’ valuation of the product. Both demands are increasing in the consumers’ WTP, and Ds is decreasing in Dc (exclusivity effect), while Dc is increasing in Ds (conformity effect). Denote by W = B, S , C the manufacturer’s possible targeting strategies, where B stands for targeting both groups of consumers, S for targeting only snobs, and C only conformists. As a manufacturer usually conducts extensive research on the customers’ preferences and purchase intentions through marketing research and/or its aggregate historical record of similar products before launching a new product, it is capable of obtaining a private signal about consumers’ WTP. (As pointed out by Desrochers et al. (2003), the manufacturer always has broader information on the current market and on market trends, which are beyond the retailer’s understanding. Buehler and Gärtner (2013) also show that manufacturers are more likely to have better projections of consumer demand than retailers via pre-launch research and development, and marketing studies). The retailer, has a limited ability to obtain such a signal and thus, can only know the distribution of the consumers’ WTP. In addition, for simplicity, the signal is assumed to be perfect, which implies that the manufacturer knows the true consumer valuation. We denote the manufacturer as i-type when the obtained signal on the WTP is i , i {h, l} . In this paper, we develop a signaling game for the supply chain, with the following sequence of events: In the first stage, with a perfect signal obtained about the consumers’ WTP, the manufacturer, as the Stackelberg leader, chooses the wholesale price w. In the second stage, the retailer, as the follower, reacts and sets the retail price p. In the third stage, the market demands for the two consumer groups and the channel members’ profits are realized. Without loss of generality, we normalize the unit production cost to zero and assume that both channel members are risk-neutral, as in Amaldoss and Jain (2005a) and Jiang et al. (2016). The notation used in the paper is summarized in Table 1. Assuming profit-maximization behavior, the optimization problems of the manufacturer and the retailer are as follows:

max[w (Ds ( i ) + Dc ( i ))], i w

{h, l},

(3)

Table 1 Notation. A: total potential market size : initial market share of snobs p: retail price (decision variable) w: wholesale price (decision variable)

{h , l} i : consumers’ WTP for the product, i b: level of exclusivity effect : level of conformity effect Dj : demands of snobs or conformists, j {s, c} m:

: price sensitivity of snobs q: demand sensitivity w.r.t. consumers’ WTP

r:

4

manufacturer’s ex ante expected profit retailer’s ex ante expected profit

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max E [(p

w )(Ds ( ) + Dc ( ))].

p

(4)

4. Equilibrium solutions In this section, we derive the equilibrium prices for the signaling game between the manufacturer and the retailer. All proofs are in the Appendix A. The equilibrium solution concept of this signaling game is the perfect Bayesian equilibrium (PBE). There are two mutually exclusive types of equilibria: separating and pooling. In the separating equilibrium, the manufacturer sets distinct wholesale prices for the two different signals received on the WTPs. Therefore, the customer’s true WTP can be revealed to the retailer through the wholesale price the manufacturer announces. For the pooling equilibrium, however, the manufacturer chooses the same wholesale price for the two different WTPs, and thus the retailer cannot infer the true WTP. In this case, multiple equilibria may arise, and the intuitive and classical equilibrium refinement rule proposed by Cho and Kreps (1987) is adopted to refine them. As it has been proved that a pooling equilibrium cannot survive the intuitive criterion for this signaling game (Jiang et al., 2016; Li et al., 2013), we focus on the separating equilibrium in this paper. Therefore, all equilibrium solutions and analyses presented in this paper are based on the retailer being perfectly able to infer the true WTP from the wholesale price. A (b b) A (1 + ) + i q (1 + ) i q (1 b) , p¯ = , d2i = A + i q , and d3i = (1 ) A + i q . With the demand functions in (1) Let p = b 1+ and (2) and for any type of ( i = h or l ), when the manufacturer targets both groups of consumers (W = B ) such that p < p < p¯ , both snobs and conformists have demands (denoted with the superscript B ); when the manufacturer targets conformists only (W = C ) such that p < p , there is no demand for snobs, and only conformists purchase the product (denoted with the superscript C); finally, when the manufacturer targets snobs only (W = S ) such that p > p¯ , there is no demand for conformists, and only snobs purchase the product (denoted with the superscript S). Therefore, the demands for the two groups of consumers are

DsB = DsC

(b

)(p

p)

1+b

,

if p < p < p¯ ,

= 0,

if p < p ,

DsS = d2i

p,

if p > p¯ ,

and

DcB =

(1 +

)(p¯ 1+b

DcC = d3i DcS

p,

= 0,

p)

,

if p < p < p¯ , if p < p , if p > p¯.

These demands correspond to the demands under the manufacturer’s consumer-targeting strategy W = B, S , C , no matter what signal i {l, h} is observed. As Jiang et al. (2016) point out, the manufacturer is better off if the retailer believes the WTP is low rather than high, because in such a case, the retailer can charge a low retail price to attract more sales, which eventually benefits the manufacturer. This implies that the manufacturer observing a high signal (i.e., h-type manufacturer) has an incentive to falsely claim that the signal is low (i.e., pretending to be an l-type manufacturer) so more sales are obtained. As a result, under the separating equilibrium, the l-type manufacturer will reduce its wholesale price to a level where the h-type manufacturer has no incentive to pretend. With demands in (1) and (2), and profit functions of the manufacturer and the retailer in (3) and (4), we can obtain equilibrium wholesale prices and selling prices for the manufacturer’s consumer-targeting strategy W = B, S , C by using signaling-game theory, b) i q , and T1 = 2(1 b + (1 + ) ) , where no matter what signal i {l, h} is received. Let d1i = ((1 b) + (b + )) A + (2 + i = h , l . We summarize the results in Proposition 1. Proposition 1. For a given manufacturer’s consumer-targeting strategy W = B, S , C , no matter what signal i {l, h} is observed, there exists a unique separating wholesale price equilibrium wiW and selling price piW given in Table 2, where wiW and z1 are given in the proof in Appendix A. To examine the impact of information on the decisions of the manufacturer and the retailer, we can easily derive the optimal wholesale price and selling price for strategy W = B, S , C under a full-information structure, i.e., where both the manufacturer and Table 2 The equilibrium wholesale price and the selling price for Strategy W. W B

wlW

whW d1h T1

S

d2h 2

C

d3h 2

min

{

{ min { min

5

d1l , T1

w lB

d2l , 2

w lS

d3l , 2

w lC

}

} }

piW (i

{h, l})

d1i T1

+ wiB

d2i 2

+ wiS

d3i 2

+ wiC

1 2

1 2

1 2

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Table 3 The equilibrium wholesale price and the selling price for Strategy W under a full-information structure. W B S

wiW

piW

d1i T1

3d1i 2T 1 3d2i 4 3d3h 4

d2i 2 d3i 2

C

the retailer know the true WTP. These strategies are given in Table 3. As seen in Tables 2 and 3, a manufacturer observing a high WTP will not distort the wholesale price (i.e., whW = whW ), as there is no additional value to be gained by setting the wholesale price unequal to the optimal wholesale price under a full-information structure. However, a manufacturer observing a low WTP may distort its wholesale price due to information asymmetry. Specifically, the manufacturer does not distort the wholesale price when it sets wlW = wlW , but it distorts the wholesale price by setting wlW = wlW . The above result suggests that, in order to reveal a small true WTP, the manufacturer needs to distort the wholesale price downward to such a level that it has no incentive to do the same after observing a high WTP. This reflects the essential core of the signaling game: imitatee must distort its decision to prevent the imitator from mimicking at the expense of the imitatee deviating from its optimal decisions; however, the imitator can obtain the optimal solutions under a full-information structure. Substituting the equilibrium solutions into (3) and (4), the profits of the manufacturer and the retailer for different consumer valuations of the product, mi , ri , i {h, l} , are obtained, and their ex-ante expected profits (before receiving the signal) are m

=

1 ( 2

mh

+

ml )

and

=

r

1 ( 2

rh

+

r l ).

Comparing the profits of the manufacturer and the retailer to those with full information, we have the following result. Proposition 2. The manufacturer is worse off from having the private information, but the retailer is better off. Consistent with the result in Jiang et al. (2016), Proposition 2 demonstrates that having the private information can lead to a reduction in the manufacturer’s profit (referred to as the signaling cost), but will benefit the retailer. The signaling cost is due to the downward distortion of the wholesale price, which equals to m m , where m is the manufacturer’s profit under a full-information structure. We now discuss the impacts of the percentage of snobs in the market ( ) and their price sensitivity ( ) on the equilibrium pricing strategies. The results can be summarized as follows. Corollary 1. The impact of and

on the wholesale and selling prices are as given in Table 4.

Corollary 1 implies that, when both consumer groups are targeted, the higher is the initial fraction of snobs in the market, then the higher the wholesale price and retail price will be. This is because the total demand in the market increases with the fraction of snobs, leading to a high wholesale price and retail price. Intuitively, a high price sensitivity will force the channel members to cut prices. In addition, when only conformists are captured, with the increase of , the demand of conformists shrinks further. Both the retailer and the manufacturer will reduce the selling price and the wholesale price, respectively, to attract more demand in the market. This sensitivity analysis offers suggestions for the manufacturer and the retailer on how to adjust their pricing strategies when facing different market situations. We now discuss the impacts of social influences b and on the equilibrium pricing strategies. With Proposition 1, we see that only when the manufacturer targets both snobs and conformists (strategy B), will these parameters affect equilibrium pricing strategies. Proposition 1 also shows that when the manufacturer receives a high signal (i = h ), there is no pricing distortion; when it receives a d low signal (i = l ), there is no pricing distortion if wlB = T1l = wlB , while there is if wlB = w lB . We define 1

Table 4 The impact of

and

on the wholesale and selling prices. The impact of

W B S C

wiW

The impact of

piW

where “ ”: positive effect; “ ”: negative effect; “–”: no effect. 6

wiW

piW

–

–

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¯1 =

d2h , d3h

¯3 = 1 ¯4 = 1

¯2 = (2d2h

d2l , d3l

A z1 Aq ( h d2l + A) z1 ( h

l )((2 + l) q (3d1h

(1 2 )(3A z1 Aq ( h (2d3h + d3l) z1 ( h l ) q (3d1h

b)(1 2 )) d1l + A (1 + )(1

b)) l )(2 + d1l + A (1 + )(1

2 ))

2 ))

,

and

,

where z1 is given in the proof of Proposition 1 in the Appendix A. The impacts of social influences b and following corollary.

are summarized in the

Corollary 2. When the manufacturer targets both groups of consumers (W = B ), (1) if i = h , both whB and phB increase with b and (2) if i = l and wlB =

d1l , T1 w lB ,

if

< min{ ¯1, 1} , and decrease with b and otherwise; if < min{ ¯2, 1} , and decrease with b and otherwise; < min{ ¯3, 1} , and otherwise decreases with b and ; p B increases with b and

both wlB and plB increase with b and

wlB increases with b and if (3) if i = l and wlB = if < min{ ¯4, 1} , and otherwise decreases with b and .

l

Corollary 2 implies that both the manufacturer and the retailer will charge a high price when facing a strong social influence, except when the snobs are very sensitive to selling price. The implication of Corollary 2 is that the vertical price competition between the manufacturer and the retailer is softened as the social influences increase, when the snobs’ sensitivity to the selling price is sufficiently low ( < min{ ¯1, ¯2, ¯3, ¯4 } ), while the vertical price competition is intensified if the snobs’ sensitivity to the selling price is sufficiently high (max{ ¯1, ¯2, ¯3, ¯4 } < < 1). Expressions of the thresholds ¯1, ¯2, ¯3 , and ¯4 show that they are closely related to . We can derive the following results. Lemma 1. ¯i = 1 if

= 1/2; ¯i > 1 if

> 1/2 and ¯i < 1 otherwise, where i = 1, 2, 3, 4 .

With Corollary 2, Lemma 1 shows that, if > 1/2 , the social influences b and positively impact the wholesale price and selling price. The reason is that when the fraction of snobs is larger than that of conformists, i.e., > 1/2 , with the increase of exclusivity b, the demand for snobs will not decrease significantly because the market share of conformists is smaller. This enables both the manufacturer and the retailer to charge high prices. In addition, with an increase in conformity , the conformists’ demand increases significantly due to the larger snob consumer group. This also triggers a high wholesale price and selling price. On the other hand, as for < 1/2 , only when < ¯i , both the manufacturer and the retailer are motivated to set high prices due to high social influences. This result suggests that with social influences, when the manufacturer and the retailer are aware that the fraction of snobs in the market is larger than that of conformists, they should raise their prices; otherwise, they should reduce the prices, except for the case when the price sensitivity of snobs is low. The implication of this result is that the channel members should have better knowledge of consumer preference before adjusting their marketing strategies. Proposition 1 presents the equilibrium solutions for the manufacturer’s three market-targeting strategies, no matter what signal i {h, l} about WTP is observed. In fact, there also exist situations where the manufacturer may have different market-targeting strategies after it observes a high or low signal. We use pair (W , W ) to represent the manufacturer’s market-targeting schedules, where the first W is for the h-type manufacturer and the second W is for the l-type manufacturer, and W = B, S , C . Six cases can be specified for the manufacturer: i) it targets two markets (strategy B) when it receives a high signal, but it targets snobs only (strategy S) or ii) conformists only (strategy C) when it observes a low signal, corresponding to market-targeting schedule (B, S ) and (B, C ) , respectively; iii) it targets snobs (strategy S) only or iv) conformists (strategy C) when it receives a high signal, but it embraces both markets (strategy B) when facing a low signal, i.e., market-targeting schedule (S, B ) and (C , B ), respectively; v) it captures snobs (strategy S) when observing a high signal, but switches to conformists (strategy C) in the case of a low signal (market-targeting strategy (S, C ) ); vi) it captures conformists (strategy C) when observing a high signal, but turns to snobs (strategy S) under a low signal, i.e., market-targeting schedule (C , S ) . We denote different market-targeting schedules with Y. Except for three marketing strategies presented in Proposition 1, Y = {(B, B ), (S, S ), (C , C )} , we have 6 additional different market-targeting schedules, Y = {(B, S ), (B, C ), (S, B ), (C , B ), (S, C ), (C , S )} . The schedule (C , S ) , however, can be ruled out. Proposition 3. The targeting schedule (C , S ) will never occur. Proposition 3 shows that the manufacturer will not target only conformists when it receives a high signal but will target only snobs when it observes a low signal. This rules out the targeting schedule (C , S ), leaving five different market-targeting schedules; (B, S ), (B , C ), (S, B ), (C , B ) , and (S, C ) . Proposition 3 not only provides a rule for the manufacturer in deciding its market-targeting strategy based on the signal it receives (high or low), but also highlights the importance of having information about the consumers’ preference. Denote the targeting schedule Y as a superscript and define

7

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Table 5 The separating wholesale and selling prices for schedule Y. Y = (B , S )

Y = (B , C )

Y = (S , B )

whY =

d1h T1

wlY = min{

phY =

3d1h 2T 1

plY =

whY =

wlY = min{

phY =

d1h T1 3d1h 2T 1

whY

d2h 2

wlY

3d2h 4

plY =

whY =

d3h 2

wlY = min{

phY =

3d3h 4

plY =

whY

=

d2h 2

wlY = min

=

3d2h 4

plY

=

phY =

Y = (C , B )

Y = (S , C )

phY

z2 T1

wlB, S =

2d1h T1

d2l 2

wlB, C

=

2d1h

z3

d3l , 2

wlS, B

=

d2h

d1l T1

z4 T1

wlC, B

T1

= d3h

wlS, C =

d2h

d1l + z5 T1 d3l 2

2

d3l 2

1 2

+ wlY d3l , 2

+

d1l , T1

d1l T1

1 2

=

d3l 2

w lB, C }

1 Y w 2 l

= min{

d1l T1

w lB, S }

w lS , B}

+ wlY d1l , T1

+

{

+

w lC, B}

1 Y w 2 l

d3l , 2

w lS, C

}

1 Y w 2 l

,

,

, z6

plY =

d2l 2

d2l , 2

and ,

where z2 z 6 are given in the proof of Proposition 4 in Appendix. Except for the separating equilibrium solutions presented in Proposition 1, with Proposition 3, the separating equilibrium solutions for the other five market-targeting schedules are presented in Proposition 4. Proposition 4. The separating equilibrium solutions for the five different market-targeting schedules are characterized in Table 5. With Proposition 1, Proposition 4 shows that the h-type manufacturer can achieve the first-best strategy and profit under its original market-targeting strategy presented in Proposition 1, but the l-type manufacturer may have to distort its wholesale price downward. In addition, the l-type manufacturer has to bear the signaling cost resulting from intentionally distorting the price to prevent the h-type manufacturer from mimicking. 5. Numerical analysis In this section, we use numerical studies to illustrate the impacts of the initial market share of snobs ( ), the level of conformist effect ( ), the level of exclusivity effect (b), and the price sensitivity of snobs ( ) on the manufacturer’s market-targeting strategy and on the wholesale price and payoffs, and we provide additional managerial insights. We set A = 10, q = 10, b = 0.2, = 0.4, = 0.2, = 0.8, h = 0.6 , and l = 0.2 (as the benchmark). 5.1. The impacts on the manufacturer’s market-targeting strategy The impacts of and , and b, and on the manufacturer’s market-targeting strategy are numerically illustrated in Figs. 1–3. To capture social influence of consumers behavior in general in luxury industry on the manufacturer’s market-targeting strategy, in this subsection, we first vary and between 0 and 1, respectively, and keep other parameters unchanged in the benchmark. A small reflects the case that the price of the luxury product is not too expensive (such as Michael Kors and Marc by Marc Jacobs) and the fraction of snob consumers in the market may be relatively low, while a large reflects the case for super-expensive luxury product and the fraction of snob consumers in the market is high. The results are illustrated in Fig. 1. There exist six market-targeting strategies under the parameters setting. When is sufficiently low, as increases, the manufacturer’s market-targeting strategy switches from (B, B ) to (B, C ) and ends with (C , C ) . The manufacturer is more likely to give up the snob market when snobs are more price sensitive. When is moderate (i.e., increases to about 0.3), with the increase of , the market-targeting strategy changes from (S, B ) to (B, B ) . This suggests that the h-type manufacturer tends to capture the conformist market as the price sensitivity of snobs increases. The reason is that the selling price decreases with (Corollary 1), which can generate a positive demand from the conformist market if the decrease in the selling price is sufficiently significant. In addition, for the same reason, the manufacturer’s targeting strategy switches from (S, S ) to (B, S ) with the increase in when is sufficiently large (about 0.8). In addition, when is sufficiently low (e.g., = 0.1), the manufacturer’s market-targeting strategy changes from (B, B ) to (S, B ), 8

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Fig. 1. Impact of

and

on the market-targeting strategy.

Fig. 2. Impact of

and b on the market-targeting strategy.

Fig. 3. Impact of

and

on the market-targeting strategy.

and then to (S, S ) as increases; when is moderate (e.g., = 0.4 ), the market-targeting strategy switches from (B, C ) to (B, B ) , to (S, B ), and then to (S, S ) ; when is sufficiently large (e.g., above 0.8), the market-targeting strategy switches from (C , C ) to (B, C ) , to (B, B ), to (B, S ) , and then to (S, S ) eventually. The results show that the manufacturer only captures the snob market if the market is sufficiently attractive. Fig. 2 illustrates the impacts of b and on the manufacturer’s market-targeting strategy. We vary and b between 0 and 1, 9

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Table 6 Examples for the targeting schedules (C , B ) and (S, C ) . Parameter space

h

= 0.25

= 0.12

=

b=

Market-targeting strategy

0.90 0.94 0.98

[0.29, 0.3] [0.3, 0.31] [0.3, 0.32]

(C , B )

0.4 0.5 0.6

[0, 0.02] [0, 0.03] [0, 0.04]

(S, C )

respectively, and keep other parameters unchanged in the benchmark. It shows that when is relatively small (e.g., = 0.2 ), as b increases, the manufacturer’s market-targeting strategy switches from (B, C ) to (C , C ) . In such a case, the snobs choose to leave the market due to the high exclusivity. When is moderate (increases to about 0.6), the market-targeting strategy switches from (B, B ) to (S, B ), and changes from (B, B ) to (B, S ) , and then to (S, S ) when is high (increases to about 0.7). Fig. 3 demonstrates the impacts of and on the manufacturer’s market-targeting strategy. We vary and between 0 and 1, respectively, and keep other parameters unchanged as in the benchmark. There are some regions where the h-type manufacturer captures both markets, but the l-type manufacturer only captures the snob market. Specifically, when is relatively large (e.g., above 0.7), with the increase of , the market-targeting strategy switches from (S, S ) , to (B, S ) , and then to (B, B ), implying that the manufacturer is motivated to capture both markets due to the high conformity. We have shown that there exist eight market-targeting strategies for the manufacturer (Propositions 1–4): six of them are illustrated in Figs. 1–3. Since strategies (C , B ) and (S, C ) are not demonstrated in the above examples, we now use two examples in Table 6 to illustrate them. We select h , b , , and , and keep other parameters unchanged as in the benchmark. Table 6 demonstrates that only when is relatively small (i.e., h is small) and is sufficiently large, does the manufacturer adopt strategy (C , B ) . In addition, only when and are both sufficiently small, and b is moderate, does the manufacturer adopt strategy (S, C ) . 5.2. The impacts on the equilibrium wholesale price and payoff Figs. 4–9 demonstrate the impacts of , , b, and on the manufacturer’s wholesale price and payoff, respectively. In Fig. 4, the market-targeting strategy changes from (C , C ) , to (B, C ) , to (B, B ) , to (B, S ) , and then to (S, S ) as increases (see Fig. 1), and each strategy corresponds to different equilibria. Fig. 4 suggests the following results. First, no matter what the signal the manufacturer receives, once the snob market is captured, the wholesale price increases with ; when only the conformist market is captured, however, the wholesale price decreases with . This is because once the snob market is targeted, a high always results in a high total demand, allowing the manufacturer to charge a high wholesale price. The intuition is that since a high corresponds to a low demand for conformists, then, when only the conformist market is captured, the manufacturer is forced to reduce the wholesale price to attract more conformists. Second, the first-best wholesale price set by the h-type manufacturer is always higher than that of the l-type manufacturer, due to the dual effects of the high WTP and signaling cost for the l-type manufacturer. Fig. 5 shows the impacts of b on w when varies. When is high (e.g., = 0.8), as b increases, the manufacturer slightly increases the wholesale price if the signal is high, but slightly decreases it if the signal is low. When becomes low (e.g., = 0.6 ), the manufacturer will charge a high wholesale price, no matter what signal it receives, as b positively affects the equilibria only when is below a certain threshold

Fig. 4. Impact of

on the wholesale price. 10

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Fig. 5. Impact of b on the wholesale price.

Fig. 6. Impact of

Fig. 7. Impact of

on the wholesale price.

on the manufacturer’s profit.

(Corollary 2). Fig. 6 shows that as increases, the manufacturer tends to slightly increase the wholesale price when observing a high signal, but to slightly decrease the wholesale price when observing a low signal. For a relatively low (i.e., = 0.6 ), the wholesale price always increases with b, regardless of the signal. Fig. 7 shows that when the market-targeting strategy is either (C , C ) or (B, C ) , the manufacturer’s profit decreases with ; its 11

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Fig. 8. Impact of b on the manufacturer’s profit.

Fig. 9. Impact of

on the manufacturer’s profit.

profit, however, increases with for market-targeting strategies (B, B ), (B , S ) , or (S, S ) . Except for (B, C ) , once the snob market is captured, the manufacturer’s profit is improved with . As seen from Figs. 8 and 9, the manufacturer’s profit decreases with and b, but increases with . Obviously, the manufacturer is better off with a high conformity, but worse off with a high price sensitivity or exclusivity. 6. Information-sharing Scheme The above analysis shows that the l-type manufacturer has to distort its wholesale price downward to signal its identity, even though the distortion hurts its profit and benefits the retailer, suggesting that having private information is not necessarily beneficial for the manufacturer. In practice, a manufacturer is sometimes willing to truthfully share its information on the market signal with its retailer, for the benefit of their long-term relationship. Under such an information-sharing scheme, the downward distortion of the wholesale price can be avoided and the manufacturer may be better off, while the retailer may be worse off. This is a similar result to Jiang et al. (2016), where the manufacturer prefers an information-sharing scheme while the retailer does not, when the manufacturer does not have a market-targeting strategy. However, unlike Jiang et al. (2016), along with considering the manufacturer’s market-targeting strategy in this paper, we will examine whether or not the manufacturer is still better off from sharing the information. 6.1. Manufacturer’s preference Under an information-sharing scheme, the market-targeting strategy for the manufacturer when it receives different signals is given as follows. Proposition 5. Seven different market-targeting strategies exist for the manufacturer under the information-sharing scheme, where Y = {(B, B ), (S, S ), (C , C ), (B, S ), (B , C ), (S, B ), (S, C )} , and strategies (C , B ) and (C , S ) are nonexistent. 12

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Table 7 The expected profits of the manufacturer and the retailer under an information-sharing scheme. Strategy F m

(B, B )

(S, S )

(C , C )

d12h + d12l T2

d22h + d22l 16

d32h + d32l 16

(B, S ) d12h T2

F r

+

d22l 16 1 2

(B, C ) d12h T2

+

d32l 16

(S, B ) d22h 16

+

d12h + d12l T2

(S, C ) d22h 16

+

d32l 16

F m

Proposition 5 implies that once the manufacturer targets the snob market when observing a low signal, it will inevitably target the snob market when observing a high signal, because consumers with high WTP are more likely to be attracted, as compared to consumers with low WTP. To examine the manufacturer’s preference regarding information sharing, we first derive the equilibrium profits (with a superb) . We script F) for the manufacturer and the retailer under an information-sharing scheme. Let T2 = 16(1 + b )(1 + + summarize the results in Lemma 2 as follows. Lemma 2. Under the information-sharing scheme (i.e., full-information scheme), the expected profits of the manufacturer and the retailer are summarized in Table 7. Comparing the manufacturer’s profits with an information-sharing scheme to those without, we can obtain its preference on information sharing under different market environments. Figs. 10–12 demonstrate the impacts of and , and b, and and on the manufacturer’s information-sharing preferences, respectively. Differing from the results in Jiang et al. (2016), Figs. 10–12 show that there are always some regions where the manufacturer benefits from no information sharing (regions denoted with NF). Although the manufacturer has to incur the signaling cost under the private-information scheme, it is still better off if its information is not shared with the retailer. The intuition is that comparing Fig. 10 to Fig. 1 (or Fig. 11 to Fig. 2, or Fig. 12 to Fig. 3), we can find that the no-sharing regions in Fig. 10 are always located near the dotted region in Fig. 1 (we denote regions with information sharing with F). For the left no-sharing region in Fig. 10, the market-targeting strategy under a private-information scheme (NF) is (B, B ) , but is (B, C ) under an information-sharing scheme (F). Although the manufacturer distorts its wholesale price downward under the private-information mechanism, the lower wholesale price enables it to capture more market shares, resulting in more profit, as compared to the case of the information-sharing scheme. 6.2. Implications of information management Discussions in Section 4 and Lemma 2 show that information can significantly impact the channel members’ decisions and payoffs. In Section 6.1, we show that the manufacturer does not always benefit from sharing its information with the retailer. Under certain conditions, it is willing to keep the information private at the expense of bearing a signaling cost. Convention suggests that the channel members generally benefit more from having full information than from uncertain information. Our study implies that the manufacturer has different information preferences if it can endogenously choose its informational capability: either a no-information (with a superscript NI), a private-information (with a superscript NF), or an information-sharing (with a superscript F) policy. We now examine the information-policy preferences of the manufacturer and the retailer in the presence of market segmentation. Under a no-information scheme, both the manufacturer and the retailer only know the mean value of the WTP, i.e., 1 µ = 2 ( h + l ). Therefore, there are only three market-targeting strategies: Y = {B, S, C } . We first present the equilibrium profits of the manufacturer and retailer under the no-information scheme (NI), considering

Fig. 10. Impact of

and

on the manufacturer’s information-sharing preference. 13

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Fig. 11. Impact of

and b on the manufacturer’s information-sharing preference.

Fig. 12. Impact of

and

on the manufacturer’s information-sharing preference.

market-targeting strategies. We have the following result. Lemma 3. Under a no-information scheme, the expected profits of the manufacturer and the retailer are summarized in Table 8.

= h Let ) on the channel members’ preferences regarding the inl . We examine the impact of the WTP difference ( changes from 0.1 to 0.6, while keeping the mean WTP unchanged, i.e., formation policy. We vary the values of h and l such that 1 ( + l ) = 0.4 . Fig. 13 illustrates the impacts of and on the manufacturer’s preferences for an information policy. 2 h Some key observations can be summarized from Fig. 13. First, the manufacturer’s preference of information policy can be divided F NI NF > m > m into five regions. Specifically, m covers a majority of the parameter space (in red). In this region, sharing information with the retailer is the best choice for the manufacturer, and a no-information policy is better than the private-information policy. The result is consistent to the fact that a full-information scheme (sharing-information scheme) generally benefits the channel members. F NF NI > m > m Second, when is relatively low (e.g., around 0.2) and is relatively large, there exists a region where m (in green), under which the manufacturer prefers a private-information policy relative to a no-information one, although sharing information with its retailer is the best policy choice. The implication is that since a large means a high h and a low l , when the signaling cost is relatively low, the expected profit may not be significantly pulled down. Therefore, the manufacturer’s profit can be higher than under a no-information policy, in which the equilibrium solutions are generated based on the mean of the WTP. Third, we find that Table 8 The expected profits of the manufacturer and the retailer under a no-information scheme. Strategy NI m

B

S

C

(d1h + d1l )2 2T

(d2h + d2l )2 32 1 NI 2 m

(d3h + d3l )2 32

NI r

14

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Fig. 13. Manufacturer’s preference for the information policy. NF F NI > m > m when is around 0.2 or 0.7, the private-information policy is preferred by the manufacturer (i.e., yellow region m ). The result is in line with those shown in Fig. 10. In fact, we know that when is about 0.2 or 0.7, the distortion of the wholesale price under a private-information policy enables the manufacturer to capture more market shares relative to the other two information policies. The effect of the increase in market share dominates the negative effect of the decrease in the wholesale price. As a result, the manufacturer is more profitable. Therefore, Fig. 13 suggests that the essential reason for preferring a private-information policy is being able to deploy varied market-targeting strategies. Finally, there also exist some regions where a no-information policy is NF NI F NI NF F > m > m > m > m preferred by the manufacturer relative to a full-information policy, i.e., m (in magenta) and m (in blue). Interestingly, this result is counterintuitive, standing in contrast to the commonsense intuition that channel members are usually more profitable under a full-information scheme than under a scheme with uncertain information. The result is driven by the manufacturer’s varied market-targeting strategies. Under certain conditions, the manufacturer would like to target both markets based on the mean of the WTP under the no-information scheme. Under the full-information policy, however, the manufacturer does not always target two market when observing a low/high WTP, i.e., strategies (B, S ), (B , C ) , and (S, B ). The corresponding expected NI NF F > m > m profit of the manufacturer for these strategies may be lower than under the no-information scheme. Region m (in blue) indicates that the information advantage from private information or full information does not always benefit the manufacturer when the market-targeting strategy is considered. We now examine the retailer’s information preference by comparing its profits: when the manufacturer shares information (F), when the manufacturer does not share information (NF), and when there is no information (NI) on the customers’ WTP. We illustrate the results in Fig. 14. In contrast to the commonsense intuition that supply chain members can generally benefit from information sharing (Huang and Wang, 2017), we find that with signal gaming, not sharing the manufacturer’s information is a dominant information policy for the retailer. This is because the distorted downward wholesale price ensures a high profit margin for the retailer. In addition, for case rNF > rNI > rF , the retailer prefers a no-information policy, and its preference is in line with the manufacturer’s. From Fig. 13, we can conclude that, under most conditions, not sharing the manufacturer’s information is an equilibrium for the supply chain with the signaling game.

Fig. 14. Retailer’s preference for the information policy. 15

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7. Conclusion and future directions Consumers’ purchasing behavior is always impacted by social influences. In this study, we examine the social influences of snobs who stop purchasing when they observe that the product is being widely consumed, because they seek exclusivity, while conformists seek to follow others’ purchasing behavior. In practice, the interactions between these two consumer groups make consumer portfolio management and the firm’s pricing decisions difficult, as consumer preference for a product is usually uncertain, and this information is often asymmetric for channel members. In general, large manufacturers can be more informative as they are able to conduct marketing research, such as forecasting programs. Their downstream retailers, however, may have no capacity to obtain the information. Considering two consumer groups with different purchasing behaviors and asymmetric information between the manufacturer and the retailer in a luxury supply chain, we investigate the pricing strategies, the manufacturer’s market-targeting strategies, as well as the information policy preferences of the manufacturer and the retailer. The main results are summarized as follows. First, we find that when two markets are captured, if the fraction of snobs is larger than one half, the social influences soften the vertical price competition between the manufacturer and the retailer, as both the manufacturer and the retailer will increase the equilibrium prices. However, if the fraction of snobs is less than one half, the social influences have a negative effect on equilibrium prices unless price sensitivity is less than a certain threshold. Second, the manufacturer may make different market-targeting schedules while receiving different signals, but it will not switch from targeting the conformist market when observing a high signal, to targeting the snob market when observing a low signal. Third, we find that the manufacturer does not always benefit from sharing its information with the retailer, even though this information sharing helps avoid the signaling cost. Fourth, the manufacturer can benefit from either a no-information, a private-information, or an informationsharing policy, depending on its market-targeting strategy. Specifically, sharing information is optimal in most cases. When the fraction of snobs is relatively low or relatively large, not sharing its private information may be preferred. When the fraction of snobs is relatively low or relatively large, and the WTP difference is not large enough, a no-information policy is the best. Lastly, not sharing the manufacturer’s information is however a dominant policy for the retailer. There are several potential extensions to this study. First, the demand sensitivity with respect to consumer valuation of the product from both markets is assumed to be the same, but it may be asymmetric in reality (Choi and Liu, 2019; Chiu et al., 2018). Taking this into account may contribute additional managerial insights to the literature in this stream. Second, we assume that the manufacturer usually has the ability to acquire consumers’ WTP, but the retailer does not. However, another situation may exist where the retailer can conduct information-acquisition activities while the manufacturer cannot (Li et al., 2018; Nalca et al., 2018). In this case, the information structure changes and a signaling game does not arise, but it would be interesting to examine the retailer’s market-targeting strategy, as well as the information preferences of the manufacturer and the retailer. Acknowledgements This work was supported by National Natural Science Foundation of China Nos. 71901173, and China Postdoctoral Science Foundation No. 3115200085, and Social Sciences and Humanities Research Council of Canada and the Natural Sciences and Engineering Research Council of Canada, and NSERC, Canada, grant RGPIN-2016-04975. Appendix A Proof of Proposition 1. With backward induction, we first solve the retailer’s problem. Under the separating equilibrium, after observing the manufacturer’s wholesale price, the retailer can perfectly infer the true WTP. When both snobs and conformists are captured, the retailer’s maximization problem is ri

= max pi

(pi

wi )(Ds ( i ) + Dc ( i )), i

{h, l},

(A.1)

where Ds ( i ) and Dc ( i ) are given in (1) and (2), with the first-order condition of (A.1) w.r.t. pi , we have

pi (wi) =

d1i w + i. T1 2

(A.2)

In anticipation of the retailer’s reaction, the manufacturer solves mi

= max wi

wi (Ds (pi (wi); i ) + Dc (pi (wi ); i )), i

{h, l},

(A.3)

which yields the optimal wholesale price without mimicking.

wi =

d1i , T1

(A.4)

and the corresponding profit is mi

=

d12i . 4T1 (1 + b )

(A.5)

Since the h-type manufacturer has an incentive to mimic the l-type manufacturer in a separating equilibrium, the l-type 16

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manufacturer has to distort its wholesale price downward to such a level that the h-type manufacturer has no incentive to pretend, h, l (a superscript) denote the retailer’s belief on the manufacturer’s type. i.e., lmh mh . Let n When it does not mimic, the h-type manufacturer’s profit is mh=

=

mh d12h 4T1 (1 + b )

,

(A.6)

but when it mimics the l-type manufacturer’s wholesale price, its profit is l mh=

=

wl (Ds (pl (wl ); h ) + Dc (pl (wl ); h)) wl (4d1h 4(1 + b)

2d1l

T1 wl ).

(A.7)

With (A.6) and (A.7), we have when wl

w l , then

l mh

mh ,

where wl is given by

z1 , T1

2d d1l wl = 1h T1

b (d1h d1l )) . in which z1 = 3d12h + d12l 4d1h d1l + 2A (1 b)(2 + With the condition wl w l , to have the maximum profit for the l-type manufacturer, the separating wholesale price is (A.8)

wl = min{wl , wl}, With (A.4), the h-type manufacturer’s wholesale price is

wh = wh =

d1h T1

(A.9)

The corresponding retail prices are obtained by substituting wi, i {h, l} into (A.2). With the same procedure, we can also obtain the separating wholesale prices for the cases where only the snob or conformist market is targeted. All the equilibrium solutions are presented in Table 2, where

wlB =

2d1h

wlS =

1 (2d2h 2 1 (2d3h 2

wlC =

d1l T1

z1

,

d2l

3d 22h + d 22l

4d2h d2l ),

d3l

3d32h + d32l

4d3h d3l ).

Proof of Proposition 2. For Strategy W = B , when i = h, m

1

mh

=

1

mh

=

= 2 ( mh + ml) ml ) . On the other hand, when i = h, m = 2 ( mh + For the other two strategies S and C, we can obtain similar results. □

d12h 4T1 (1 + b ) rh

=

; when i = l,

ml

rh , and when i = l,

ml rl

=

d12l 4T1 (1 + b )

Proof of Corollary 1. For Strategy W = B , the derivatives of the wholesale price and selling price with respect to whB whB phB

If wlB =

=

A (b + ) T1

phB

> 0,

=

2d1h (1 + ) T12

< 0,

=

3d1h (1 + ) T12

< 0.

=

3A (b + ) 2T1

> 0,

d1l , T1 wlB wlB plB plB

=

A (b + ) T1

=

(2d1h

=

3A (b + ) 2T1

=

> 0, d1l

z1 )(1 + ) T12

< 0,

> 0,

3d1l (1 + ) T12

< 0.

If wlB = w lB ,

17

. Therefore,

rl . Therefore,

and

r

are

r.

Transportation Research Part E 133 (2020) 101822

Q. Zhang, et al. wlB wlB plB plB

A (b + )( z1 (d1h T1 z1

=

2(2d1h

=

d1l

d1l))

z1 )(1 + )

(2d1h

=

< 0,

T12

A (b + )(3 z1 (d1h 2T1 z1

=

> 0,

d1l

d1l ))

> 0,

3 z1 )(1 + )

< 0.

T12

Similarly, for Strategy W = S , it is easy to prove that the equilibrium pricing strategies increase with , but decrease with . For Strategy W = C , the equilibrium pricing strategies decrease with , but are independent of . □ Proof of Corollary 2. When the manufacturer targets both groups of consumers (W = B ), (1) if i = h , the derivatives of the wholesale price and selling price with respect to b and whB

=

2(1 + )(d2h T12

d3h)

,

=

3(1 + )(d2h T12

d3h)

,

=

2(1

b)(d2h T12

d3h)

,

=

3(1

b)(d2h T12

d3h)

,

b phB b whB phB

which are positive if (3) If i = l and

wlB b

=

where t1 =

wlB

=

d1l , it is easy T1 w lB , then

d2l ) z1 + (

d2l ) z1

(

wB

also find that l > 0 if Also, we have

plB b

=

where t3 =

to prove that

wlB b

,

wlB

,

plB b

,

plB

are positive if

< min{ ¯2, 1} , where ¯2 =

d2l . d3l

l ) q (3d1h

h

l ) q (3d1h

h

d1l

d1l + A (1 + )(1

A (1

b)(1

wlB

2 )) < 0, t2 =. Thus,

b

> 0 if

t2 . t1

< ¯3 =

Similarly, we

2 )) > 0

< ¯3 .

(1 + )(t3 + t4 ) , T12 z1 z1 (2d3h + d3l ) + (

(2d2h + d2l ) z1 verified that

d2h . d3h

2(1 + )(t1 + t2) , T12 z1

(A + 2d2h

(2d2h

and

< min{ ¯1, 1} , where ¯1 =

(2) If i = l and wlB =

are

plB

(

h

l ) q (3d1h

h

l ) q (3d1h

d1l

d1l + A (1 + )(1 A (1

b)(1

2 )) < 0, t4 =. Thus,

plB b

> 0 if

< ¯4 =

t4 . t3

Similarly, it is

2 )) > 0

< ¯4 . □

> 0 if

Proof of Lemma 1. Substituting = 1/2 into ¯i, i = 1, 2, 3, 4 , we can easily verify that ¯i = 1. In addition, with expressions of ¯1, ¯2, ¯3 , and ¯4 , we can show that ¯i > 1 if > 1/2 and ¯i < 1 if < 1/2 . □ Proof of Proposition 3. If Strategy (C , S ) exists, it means that conditions Ds ( h) < 0, Dc ( h ) > 0, Ds ( l ) > 0 , and Dc ( l ) < 0 should d hold. wl = T1l is the optimal wholesale price when the retailer knows that the true WTP is low, and Dc ( l ) is the corresponding 1 demand. The distorted wholesale price under private information satisfies wl wl , which gives Dc ( l ) < Dc ( l ) < 0 . Then Ds ( h) < 0, Dc ( h ) > 0 , and Dc ( l ) < 0 require

y1 = ((4 b + 2 + b y2 =

((3b +

2

y3 =

((3b +

2

) d3h + A (1 + )(1

2 ))

(b 2 + 3 b + 4

2b) d2h + Ab (1

+ 4 + 2 ) d3h

A (1 + )(1

2 )) + (4b + b + 2

) d2h

+ 4 + 2 ) d3l

A (1 + )(1

2 )) + (4b + b + 2

) d2l

A (1 A (1

b)(1 b)(1 b)(1

2 ) > 0, 2 ) < 0,

and

2 ) > 0.

2i ((3b + 2 + 4 + 2 ) d3i A (1 + )(1 2 )), m2i (4b + b + 2 ) d2i A (1 b)(1 2 ) and 1i Let m1i . Then m1i y2 and y3 can be rewritten as y2 = m1h + m2h and y3 = m1l + m2l , respectively. To ensure y2 < 0 and y3 > 0, should satisfy > 1h and < 1l simultaneously, which requires 1h < 1l . It can be proved that 1i 1 1 1 is increasing with i if < 2 , but decreasing with i if > 2 . Therefore, should satisfy > 2 . Meanwhile, m2i is increasing with ,

m

and m2i | = 1 > 0 , which gives m2i > 0 for 2 < < 1. With m1i < 0 , we obtain that 2 Then, the parameter spaces to guarantee y2 < 0 and y3 > 0 are 1

18

1i

> 0.

Transportation Research Part E 133 (2020) 101822

Q. Zhang, et al.

min{

1h ,

1} <

< min{ 1l, 1}

and

1 < 2

< 1.

4 ) d3h + A (1 + )(1 2 ), m4 (b2 + 3 b + 4 2b) d2h + Ab (1 b)(1 2 ) > 0 and 2 Let m3 (4 b + 2 + b . Then m3 y1 is rewritten as y1 = m3 + m4 . y1 > 0 requires: either (1) m3 > 0 and > 2 or (2) m3 < 0 and < 2 . Condition (1) gives < and > 2 , and condition (2) gives > and < 2 , where

m

=

(4b + b

+ 2) h q + A (4b + b + 3) 1 > . A (4b + b + + 4) 2

To ensure y2 < 0 and y3 > 0 , there may exist two cases that can simultaneously satisfy y1 > 0, y2 < 0 and y3 > 0 . 1 Case (a): 2 < < , min{ 1h, 1} < < min{ 1l, 1} and > 2 . Case (b): < < 1, min{ 1h, 1} < < min{ 1l, 1} and < 2 . 1 However, for case (a), 2 is increasing in for 2 < < . Then, satisfied. Case (a) does not exist. For case (b), m4 is decreasing with . Then, m4 < m4 | = 1 < 0 for < 2 and case (b) also does not exist. Therefore, Strategy (C , S ) is ruled out. □

2

>

2| = 1 2

> 1. Therefore, the condition

< 1, which gives

2

< 0 . The condition

> <

2

2

cannot be

fails to hold,

Proof of Proposition 4. We present the detailed derivation for market-targeting schedule (B, S ) as an example in this proof and summarize the equilibrium results in Table 5 for the other market-targeting schedules (B, C ), (S , B ), (C , B ) , and (S, C ) , as their derivation procedures are similar. In this schedule, the l-type manufacturer that targets the snob market has to set a distorted wholesale price to separate itself from the h-type manufacturer that targets the snob and conformist markets. For the l-type manufacturer that targets the snob market only, its selling price reaction is

pl (wl ) =

d2l + wl . 2

(A.10)

If the the h-type manufacturer does not mimic, to target both the snob and conformist markets, its profit is mh

=

d12h , 4T1 (1 + b )

(A.11)

while when it mimics the l-type manufacturer who targets the snob market only, its profit is l mh =wl (Ds (pl (wl ); h ) w =4 (1 +l b) (2(2 d1h

+ Dc (pl (wl ); h)) T1 (d2l + wl )),

where Ds (pl (wl ); h ) and Dc (p1 (wl ); h) are given in (1) and (2), respectively. To ensure the h-type manufacturer has no incentive to pretend, it requires that

wl

wl =

2d1h T1

d2l 2

l mh

mh ,

which yields

z2 , T1

b) d2h + A (1 b)(1 2 )) . where z2 = 3 2d12h + T12 d22l /4 2 T1 d2l ((2 + To extract the maximum profit based on separating its type, the l-type manufacturer’s separating wholesale price is

wl = min

{

}

d2l , wl , 2

(A.12)

and the corresponding retail price is obtained by substituting (A.12) into the retail price reaction in (A.10). In addition, the the h-type manufacturer’s separating wholesale price is its first-best price. Substituting this price into the retail price reaction in (A.2), we can obtain its retail price. Following the same procedures, the equilibrium solutions for other four schedules, (B, C ), (S , B ), (C , B ) , and (S, C ) , are derived and summarized in Table 5, where z 3 z 6 are given as follows:

z3 = 3d12h + T12 d32l /4 z 4 = 3T12 d 22h /4 + z5 = 3T12 d32h/4 + z 6 = 3d 22h +

2d 2 3l

2T1 d3l ((2 +

2d 2 1l d12l

2 T1 d2h ((2 + 2T1 d3h ((2 +

b) d3h

A (1 + )(1

b) d2l + A (1 b) d3l

2 )),

b)(1

A (1 + )(1

2 )), 2 )),

4 d2h d3l.

Proof of Proposition 5. Under an information-sharing scheme, when the manufacturer receives a high and low signal, the demand difference from the snob market is

19

Transportation Research Part E 133 (2020) 101822

Q. Zhang, et al.

Ds= DsB ( h ) =

( h

DsB ( l )

2 l ) q (b + 3b

2b + 4 (2 + 4b + b 2T1 (1 + b )

) )

> 0.

This means that when the manufacturer captures the snob market when receiving a low signal, it is necessary for the manufacturer to target the snob market when receiving a high signal. That is, market-targeting schedules (C , B ) and (C , S ) will never occur. □ Proof of Lemma 2. Under an information-sharing strategy, both the manufacturer and the retailer know the true WTP. As for Strategy (B, B ) , the equilibrium retail price reaction and the wholesale price are the same as those in (A.2) and (A.4), and the manufacturer’s profit for each WTP type is given in (A.5). Thus, the ex ante expected profit for the manufacturer is m

=

d12h + d12l , 8T1 (1 + b )

and the retailer’s ex ante expected profit is r

=

d12h + d12l . 16T1 (1 + b )

By the same token, the equilibrium profits for the other six cases can be obtained, as given in Lemma 2. □ Proof of Lemma 3. When the manufacturer does not have any information about the WTP, both channel members only know the 1 mean WTP, i.e., E [ ] = µ = 2 ( h + l ) . With the same procedure as presented in the proof of Lemma 2, the corresponding equilibrium profits are obtained. □

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